pcalg (version 2.7-12)

visibleEdge: Check visible edge.

Description

Check if the directed edge from x to z in a MAG or in a PAG is visible or not.

Usage

visibleEdge(amat, x, z)

Value

TRUE if edge is visible, otherwise FALSE.

Arguments

amat

Adjacency matrix of type amat.pag

x,z

(integer) position of variable \(x\) and \(z\), respectively, in the adjacency matrix.

Author

Diego Colombo

Details

All directed edges in DAGs and CPDAGs are said to be visible. Given a MAG M / PAG P, a directed edge A -> B in M / P is visible if there is a vertex C not adjacent to B, such that there is an edge between C and A that is into A, or there is a collider path between C and A that is into A and every non-endpoint vertex on the path is a parent of B. Otherwise A -> B is said to be invisible. (see Maathuis and Colombo (2015), Def. 3.1)

References

M.H. Maathuis and D. Colombo (2015). A generalized backdoor criterion. Annals of Statistics 43 1060-1088.

See Also

backdoor

Examples

amat <- matrix(c(0,3,0,0, 2,0,2,3, 0,2,0,3, 0,2,2,0), 4,4)
colnames(amat) <- rownames(amat) <- letters[1:4]
if(require(Rgraphviz)) {
plotAG(amat)
}

visibleEdge(amat, 3, 4) ## visible
visibleEdge(amat, 2, 4) ## visible
visibleEdge(amat, 1, 2) ## invisible